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// Copyright (c) 2003,2004,2006 INRIA Sophia-Antipolis (France). // All rights reserved. // // This file is part of CGAL (www.cgal.org). // // $URL: https://github.com/CGAL/cgal/blob/v6.1/Apollonius_graph_2/include/CGAL/Apollonius_graph_2/Incircle_C2.h $ // $Id: include/CGAL/Apollonius_graph_2/Incircle_C2.h b26b07a1242 $ // SPDX-License-Identifier: GPL-3.0-or-later OR LicenseRef-Commercial // // // Author(s) : Menelaos Karavelas #ifndef CGAL_APOLLONIUS_GRAPH_2_INCIRCLE_C2_H #define CGAL_APOLLONIUS_GRAPH_2_INCIRCLE_C2_H #include #include #include #include #include namespace CGAL { namespace ApolloniusGraph_2 { //-------------------------------------------------------------------- template< class K > class Sign_of_distance_from_bitangent_line_2 { public: typedef Bitangent_line_2 Bitangent_line; typedef typename K::Site_2 Site_2; typedef Inverted_weighted_point_2 Inverted_weighted_point; typedef typename K::FT FT; typedef typename K::Sign Sign; public: inline Sign operator()(const Bitangent_line& bl, const Site_2& q, const Field_with_sqrt_tag&) const { #ifdef AG2_PROFILE_PREDICATES ag2_predicate_profiler::distance_from_bitangent_counter++; #endif FT a = bl.a1() + bl.a2() * CGAL::sqrt(bl.delta()); FT b = bl.b1() + bl.b2() * CGAL::sqrt(bl.delta()); FT c = bl.c1() + bl.c2() * CGAL::sqrt(bl.delta()); FT r = a * q.x() + b * q.y() + c - q.weight() * bl.d(); return CGAL::sign(r); } inline Sign operator()(const Bitangent_line& bl, const Site_2& q, const Integral_domain_without_division_tag&) const { #ifdef AG2_PROFILE_PREDICATES ag2_predicate_profiler::distance_from_bitangent_counter++; #endif FT A = bl.a1() * q.x() + bl.b1() * q.y() + bl.c1() - q.weight() * bl.d(); FT B = bl.a2() * q.x() + bl.b2() * q.y() + bl.c2(); return sign_a_plus_b_x_sqrt_c(A, B, bl.delta()); } }; //-------------------------------------------------------------------- template< class K > class Sign_of_distance_from_CCW_circle_2 { public: typedef Bitangent_line_2 Bitangent_line; typedef Inverted_weighted_point_2 Inverted_weighted_point; typedef typename K::FT FT; typedef typename K::Sign Sign; public: inline Sign operator()(const Bitangent_line& bl, const Inverted_weighted_point& v, const Field_with_sqrt_tag&) const { FT a = bl.a1() + bl.a2() * CGAL::sqrt(bl.delta()); FT b = bl.b1() + bl.b2() * CGAL::sqrt(bl.delta()); FT c = bl.c1() + bl.c2() * CGAL::sqrt(bl.delta()); FT r = a * v.x() + b * v.y() + c * v.p() - v.weight() * bl.d(); return CGAL::sign(r); } inline Sign operator()(const Bitangent_line& bl, const Inverted_weighted_point& v, const Integral_domain_without_division_tag&) const { FT A = bl.a1() * v.x() + bl.b1() * v.y() + bl.c1() * v.p() - v.weight() * bl.d(); FT B = bl.a2() * v.x() + bl.b2() * v.y() + bl.c2() * v.p(); return sign_a_plus_b_x_sqrt_c(A, B, bl.delta()); } }; template < class Weighted_point > class Weighted_point_less_than { public: inline bool operator()(const Weighted_point& p1, const Weighted_point& p2) const { if ( p1.x() == p2.x() ) { return p1.y() < p2.y(); } return p1.x() < p2.x(); } }; template < class K, class MTag > class Vertex_conflict_2 { public: typedef K Kernel; typedef MTag Method_tag; typedef typename K::Point_2 Point_2; typedef typename K::Site_2 Site_2; typedef Weighted_point_inverter_2 Weighted_point_inverter; typedef Inverted_weighted_point_2 Inverted_weighted_point; typedef Bitangent_line_2 Bitangent_line; typedef Voronoi_radius_2 Voronoi_radius; typedef typename K::FT FT; typedef typename K::Orientation Orientation; typedef typename K::Sign Sign; typedef typename K::Bounded_side Bounded_side; typedef Bounded_side_of_CCW_circle_2 Bounded_side_of_CCW_circle; typedef Sign_of_distance_from_bitangent_line_2 Sign_of_distance_from_bitangent_line; typedef Sign_of_distance_from_CCW_circle_2 Sign_of_distance_from_CCW_circle; private: inline Orientation orientation(const Bitangent_line& l, const Point_2& p, const Field_with_sqrt_tag&) const { FT A = l.a1() * p.x() + l.b1() * p.y() + l.c1(); FT B = l.a2() * p.x() + l.b2() * p.y() + l.c2(); FT P = A + B * CGAL::sqrt(l.delta()); return CGAL::sign(P); } inline Orientation orientation(const Bitangent_line& l, const Point_2& p, const Integral_domain_without_division_tag&) const { FT A = l.a1() * p.x() + l.b1() * p.y() + l.c1(); FT B = l.a2() * p.x() + l.b2() * p.y() + l.c2(); return sign_a_plus_b_x_sqrt_c(A, B, l.delta()); } inline Orientation orientation(const Bitangent_line& l, const Inverted_weighted_point& u) const { FT A = l.a1() * u.x() / u.p() + l.b1() * u.y() / u.p() + l.c1(); FT B = l.a2() * u.x() / u.p() + l.b2() * u.y() / u.p() + l.c2(); FT P = A + B * CGAL::sqrt(l.delta()); return CGAL::sign(P); } public: typedef Sign result_type; typedef Site_2 argument_type; inline Sign operator()(const Site_2& p1, const Site_2& p2, const Site_2& p3, const Site_2& q) const { #ifdef AG2_PROFILE_PREDICATES ag2_predicate_profiler::incircle_counter++; #endif // Method_tag tag; Weighted_point_inverter inverter(p1); Inverted_weighted_point u2 = inverter(p2); Inverted_weighted_point u3 = inverter(p3); Voronoi_radius vr_123(u2, u3); Bounded_side bs = Bounded_side_of_CCW_circle()(vr_123, tag ); if ( bs != ON_UNBOUNDED_SIDE ) { return NEGATIVE; } Inverted_weighted_point v = inverter(q); Bitangent_line blinv_23(u2, u3); Sign s = Sign_of_distance_from_CCW_circle()(blinv_23, v, tag); return s; } inline Sign operator()(const Site_2& p1, const Site_2& p2, const Site_2& q) const { Method_tag tag; // Bitangent_line bl_21(p2, p1); Sign s = Sign_of_distance_from_bitangent_line()(bl_21, q, tag); if ( s != ZERO ) { return s; } Bitangent_line bl1_perp = bl_21.perpendicular(p1.point()); Bitangent_line bl2_perp = bl_21.perpendicular(p2.point()); Orientation o1 = orientation(bl1_perp, q.point(), tag); Orientation o2 = orientation(bl2_perp, q.point(), tag); CGAL_assertion( o1 != COLLINEAR || o2 != COLLINEAR ); if ( o1 == o2 ) { return POSITIVE; } return NEGATIVE; } }; //-------------------------------------------------------------------- } //namespace ApolloniusGraph_2 } //namespace CGAL #endif // CGAL_APOLLONIUS_GRAPH_2_INCIRCLE_C2_H